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<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.stat_tut.variates"></a><a class="link" href="variates.html" title="Random Variates and Distribution Parameters">Random Variates and Distribution
      Parameters</a>
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<p>
        <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">Random variates</a>
        and <a href="http://en.wikipedia.org/wiki/Parameter" target="_top">distribution parameters</a>
        are conventionally distinguished (for example in Wikipedia and Wolfram MathWorld
        by placing a semi-colon after the <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">random
        variate</a> (whose value you 'choose'), to separate the variate from
        the parameter(s) that defines the shape of the distribution.
      </p>
<p>
        For example, the binomial distribution has two parameters: n (the number
        of trials) and p (the probability of success on one trial). It also has the
        <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">random variate</a>
        <span class="emphasis"><em>k</em></span>: the number of successes observed. This means the
        probability density/mass function (pdf) is written as <span class="emphasis"><em>f(k; n, p)</em></span>.
      </p>
<p>
        Translating this into code the <code class="computeroutput"><span class="identifier">binomial_distribution</span></code>
        constructor therefore has two parameters:
      </p>
<pre class="programlisting"><span class="identifier">binomial_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
</pre>
<p>
        While the function <code class="computeroutput"><span class="identifier">pdf</span></code> has
        one argument specifying the distribution type (which includes its parameters,
        if any), and a second argument for the <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">random
        variate</a>. So taking our binomial distribution example, we would write:
      </p>
<pre class="programlisting"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">binomial_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;(</span><span class="identifier">n</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">k</span><span class="special">);</span>
</pre>
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